1. Field of the Invention
Implementations of various technologies described herein generally relate to methods and systems for estimating velocities with uncertainty.
2. Description of the Related Art
The following descriptions and examples are not admitted to be prior art by virtue of their inclusion within this section.
When drilling a well, a fluid is inserted into a well-bore to maintain the integrity of the well-bore wall. If the pressure of the fluid in the well-bore is lower than the pore pressure (the pressure of the fluids in the formation surrounding the well), the fluids in the formation could enter the well-bore.
The fluid inserted into the well-bore to maintain the integrity of the well-bore wall is known as a mud. The mud is a fluid with suspended particles. A mud-weight is the amount of pressure that the mud applies to the well-bore wall. To prevent a kick, the driller uses an appropriate mud-weight. A kick is a collapse of the well-bore wall due to fluids with a pore pressure greater than the pressure within the well-bore. In one such scenario, flammable liquids, such as gas, could enter the well-bore and ignite.
Typically, the pore pressure increases as the well-bore is dug. Accordingly, the mud weight may be increased. However, the mud weight may not exceed a minimum stress of the well-bore. The minimum stress is an amount of pressure against the well-bore wall that may induce fractures in the surrounding formation. A fracture may lead to the loss of drilling fluid, which is very costly.
An increase in mud pressure increases the pressure along the entire length of the well-bore wall. If the mud pressure is higher than the minimum stress in a more shallow part of the well-bore, the well-bore wall may fracture. As such, a range of pressure is maintained within the well-bore that is greater than the pore pressure but less than the minimum stress. The pore pressure and the minimum stress provide a mud-weight pressure window, and this window may be used to decide the depth of casing points.
The casing points are depths within the well-bore where casing shoes are inserted. For example, when the pore pressure at a lower well-bore depth exceeds the minimum stress at a more shallow depth, a casing shoe may be inserted to protect the integrity of the well-bore wall at the more shallow depth.
The casing shoes are steel tubes that are cemented into place to protect the integrity of the well. Once the casing shoe is inserted, the mud-weight may be increased at the lower depth without inducing fractures at the more shallow depth. The casing shoes are very expensive and are typically ordered ahead of time due to the logistics involved in planning and digging wells.